📚 KS3 AQA Psychology: Quick Reference Handbook of Formulas and Theorems | KS3 AQA 心理学：公式定理速查手册
This handbook compiles the essential formulas, laws, and theorems you need for KS3 AQA Psychology. From memory models and social influence principles to research correlation and perceptual laws, each concept is broken down into clear, revisable references to strengthen your understanding and exam readiness.
本手册汇集了KS3 AQA心理学所需的核心公式、定律和定理。从记忆模型、社会影响原理到研究相关性和知觉定律，每个概念都分解为清晰易查的参考条目，助你巩固理解、高效备考。
1. Memory: Multi-Store Model & Miller’s Magic Number | 记忆：多贮存模型与米勒的魔力数字
Atkinson and Shiffrin proposed the multi-store model of memory, which describes three separate but linked stores: sensory memory, short-term memory (STM), and long-term memory (LTM). Information flows from sensory memory, through attention, into STM, and with rehearsal it can be transferred to LTM.
阿特金森和谢夫林提出了记忆的多贮存模型，描述了三个独立又相互关联的贮存：感觉记忆、短时记忆（STM）和长时记忆（LTM）。信息通过注意从感觉记忆进入短时记忆，再通过复述可以转入长时记忆。
Miller’s magic number states that the capacity of STM is about 7 ± 2 chunks. A chunk is a meaningful unit of information, and chunking allows us to hold more information by grouping smaller bits into larger, meaningful wholes.
米勒的魔力数字指出，短时记忆的容量约为7±2个组块。一个组块是有意义的信息单元，通过将较小的信息片段组合成更大的、有意义的整体，组块化能让我们容纳更多信息。
| Store 贮存 | Duration 持续时间 | Capacity 容量 | Encoding 编码 |
|---|---|---|---|
| Sensory memory 感觉记忆 | <1 sec (iconic) / 2-3 sec (echoic) 图像<1秒/声像2-3秒 | Very large 非常大 | Modality-specific 感觉通道特有 |
| STM 短时记忆 | 18-30 sec without rehearsal 不复述持续18-30秒 | 7 ± 2 chunks 7±2个组块 | Mainly acoustic 主要为听觉编码 |
| LTM 长时记忆 | Unlimited 无限 | Unlimited 无限 | Mainly semantic 主要为语义编码 |
2. Ebbinghaus Forgetting Curve: The Exponential Decay of Memory | 艾宾浩斯遗忘曲线：记忆的指数衰减
Hermann Ebbinghaus studied memory using nonsense syllables and discovered that forgetting follows an exponential curve. Memory loss occurs most rapidly in the first 20 minutes after learning, then gradually levels off over days. Relearning and spaced repetition can counteract this decay.
赫尔曼·艾宾浩斯使用无意义音节研究记忆，发现遗忘遵循指数曲线。记忆丧失在学习后最初20分钟内最快，然后数天内逐渐放缓。再学习和间隔重复可以对抗这种衰减。
He measured saving using the formula: Saving (%) = (T1 – T2) / T1 × 100, where T1 is the original learning time and T2 is the relearning time after a retention interval. A higher saving percentage indicates stronger retention.
他用节省分数来衡量，公式为：节省百分比(%) = (T1 – T2) / T1 × 100，其中T1为初始学习时间，T2为保持间隔后的再学习时间。节省百分比越高，表明保持越牢固。
Saving (%) = (T₁ – T₂) / T₁ × 100
3. Social Influence: Bystander Effect & Social Loafing | 社会影响：旁观者效应与社会惰化
The bystander effect states that the more people present, the less likely any one person will help a victim. This is due to diffusion of responsibility and pluralistic ignorance. Latane and Darley’s decision model shows that before helping, five steps must be passed: noticing, interpreting as emergency, assuming responsibility, knowing how to help, and implementing help.
旁观者效应指出，在场人数越多，个体伸出援手的可能性就越小。原因在于责任分散和多数无知。拉塔奈和达利的决策模型显示，助人前须经历五个步骤：注意到事件、解读为紧急状况、承担责任、知道如何帮助、实施帮助。
Social loafing, first described by Ringelmann, is the tendency for individuals to exert less effort when working in a group than when working alone. As group size increases, individual productivity often decreases unless individual contributions are identifiable.
社会惰化最早由林格尔曼描述，指个体在团体中工作所付出的努力少于独自工作时。随着团体规模扩大，个体生产力往往下降，除非个人贡献可以被识别。
| Social Law 社会定律 | Core Principle 核心原则 | Key Study 关键研究 |
|---|---|---|
| Bystander Effect 旁观者效应 | Help likelihood decreases as bystander numbers increase. 旁观者越多，助人可能性越低。 | Latane & Darley smoke-filled room study 拉塔奈和达利充满烟雾的房间研究 |
| Social Loafing 社会惰化 | Individual effort drops in group tasks. 个体在团体任务中努力下降。 | Ringelmann rope-pulling experiment 林格尔曼拔河实验 |
4. Obedience: Milgram’s Agency Theory | 服从：米尔格拉姆的代理理论
Stanley Milgram’s obedience experiments revealed that ordinary people could deliver what they believed to be lethal shocks under authority pressure. His agency theory explains that in an agentic state, individuals see themselves as agents carrying out orders, thus feeling no personal responsibility. In contrast, the autonomous state involves acting on one’s own free will.
斯坦利·米尔格拉姆的服从实验表明，普通人在权威压力下会实施他们相信是致命的电击。他的代理理论解释，处于代理状态的个体将自己视为执行命令的工具，因此不感到个人责任。相反，自主状态则是按自己的自由意志行动。
The shift from autonomous to agentic state is called the agentic shift. Factors increasing obedience include physical proximity of authority, legitimacy of the setting, and lack of defiant peers. This principle helps explain real-world atrocities like those seen in Nazi Germany.
从自主状态转为代理状态称为代理转换。增强服从的因素包括权威的物理接近度、环境合法性以及缺乏反抗同伴。这一原理有助于解释现实世界中的暴行，如纳粹德国的行径。
5. Cognitive Biases: Anchoring and Confirmation Bias | 认知偏差：锚定效应与确认偏误
Anchoring bias describes how our estimates are influenced by an initial reference point, or anchor, even if that anchor is arbitrary. Our final judgment is the anchor plus an insufficient adjustment: Final Estimate = Anchor + Adjustment. Typically, the adjustment is too small, pulling the estimate toward the anchor.
锚定效应描述判断如何受到初始参照点（锚）的影响，即使该锚是随意的。最终判断是锚加上不充分的调整：最终估计 = 锚值 + 调整。通常调整幅度过小，将估计值拉向锚点。
Confirmation bias is the tendency to seek, interpret, and remember information that confirms our pre-existing beliefs, while ignoring contradictory evidence. In experiments, participants give more weight to data supporting their views and criticise disconfirming evidence.
确认偏误指人倾向于寻找、解读并记住能证实自己既有信念的信息，而忽略矛盾证据。实验中，被试会更重视支持自己观点的数据，并挑剔反驳证据。
6. Research Methods: Variables and Correlation Coefficient | 研究方法：变量与相关系数
In psychological experiments, the independent variable (IV) is the factor manipulated by the researcher, and the dependent variable (DV) is the factor measured. Extraneous variables must be controlled to establish cause and effect. Operationalisation defines how variables are precisely measured.
在心理学实验中，自变量（IV）是研究者操纵的因素，因变量（DV）是被测量的因素。须控制额外变量以确立因果关系。操作化定义变量如何被精确测量。
The Pearson product-moment correlation coefficient (r) quantifies the strength and direction of a linear relationship between two variables. Its value ranges between -1 and +1. A positive r means as one variable increases, the other tends to increase; a negative r indicates an inverse relationship. r = 0 suggests no linear correlation.
皮尔逊积差相关系数（r）量化两个变量间线性关系的强度和方向。其值范围在 -1 到 +1 之间。r 为正表示一个变量增加，另一个也趋于增加；r 为负表示反向关系。r = 0 表示无线性相关。
-1 ≤ r ≤ +1
Researchers must also consider the mean, median, and mode for central tendency, as well as range and standard deviation for dispersion. A scatterplot with a line of best fit visually represents a correlation. However, correlation does not imply causation.
研究人员还需考虑集中量数（平均数、中位数、众数）以及离散量数（全距和标准差）。带最佳拟合线的散点图能直观呈现相关。然而，相关不等于因果关系。
7. Classical and Operant Conditioning: Learning Laws | 经典与操作条件作用：学习定律
Classical conditioning, developed by Ivan Pavlov, involves learning through association. A neutral stimulus (NS) is paired with an unconditioned stimulus (UCS) that naturally produces an unconditioned response (UCR). After repeated pairings, the NS becomes a conditioned stimulus (CS), eliciting a conditioned response (CR).
经典条件作用由伊万·巴甫洛夫提出，是通过联系进行的学习。中性刺激（NS）与无条件刺激（UCS）反复配对，UCS自然地引发无条件反应（UCR）。经过多次配对后，NS变为条件刺激（CS），引发条件反应（CR）。
Key laws include extinction (CR weakens when CS is presented without UCS), spontaneous recovery (CR reappears after a rest period), stimulus generalisation (similar stimuli trigger CR), and discrimination (only the specific CS elicits CR).
关键定律包括消退（当CS单独呈现而不伴随UCS时CR减弱）、自然恢复（休息后CR重新出现）、刺激泛化（相似刺激也能引发CR）和辨别（只有特定CS能引发CR）。
Operant conditioning, formulated by B.F. Skinner, is learning through consequences. Positive reinforcement (adding pleasant stimulus) increases a behaviour; negative reinforcement (removing unpleasant stimulus) also increases a behaviour. Punishment (adding unpleasant or removing pleasant stimulus) decreases a behaviour. Behaviour is shaped by reinforcement schedules: continuous, fixed ratio, variable ratio, fixed interval, and variable interval.
操作条件作用由B.F.斯金纳提出，是通过后果进行的学习。正强化（加入愉快刺激）增加行为；负强化（移除不愉快刺激）也增加行为。惩罚（加入不愉快或移除愉快刺激）减少行为。行为由强化程式塑造：连续强化、固定比率、可变比率、固定时距和可变时距。
8. Sensation & Perception: Weber’s Law and Perceptual Constancies | 感觉与知觉：韦伯定律与知觉恒常性
Weber’s Law describes the just noticeable difference (JND) — the minimum change in a stimulus that can be detected. The law states that the JND is a constant proportion of the original stimulus intensity: ΔI / I = k, where I is the initial stimulus intensity, ΔI is the JND, and k is the Weber fraction.
韦伯定律描述了最小可觉差（JND）——能被察觉的最小刺激变化量。该定律表明JND 是初始刺激强度的一个恒定比例：ΔI / I = k，其中 I 为初始刺激强度，ΔI 为最小可觉差，k 为韦伯分数。
ΔI / I = k
Perceptual constancies allow us to perceive objects as stable despite changes in sensory input. Size constancy means an object’s perceived size remains the same as its distance changes; shape constancy keeps the shape stable when the viewing angle changes; colour constancy maintains perceived colour under different lighting. These constancies rely on contextual cues and top-down processing.
知觉恒常性使我们能在感觉输入变化时仍将物体知觉为稳定。大小恒常性指物体距离改变时，其知觉大小保持不变；形状恒常性在视角变化时保持形状稳定；颜色恒常性在不同光照下保持颜色感知不变。这些恒常性依赖情境线索和自上而下的加工。
9. Developmental Psychology: Piaget’s Stages and Vygotsky’s ZPD | 发展心理学：皮亚杰阶段论与维果茨基的最近发展区
Jean Piaget proposed four stages of cognitive development, each with distinct intellectual abilities. The sensorimotor stage (0-2 years) involves learning through senses and actions; preoperational (2-7 years) features symbolic thinking and egocentrism; concrete operational (7-11 years) brings logical thought about concrete events; formal operational (11+ years) enables abstract reasoning.
让·皮亚杰提出四个认知发展阶段，各阶段具有独特的智力能力。感知运动阶段（0-2岁）通过感觉和动作学习；前运算阶段（2-7岁）表现为符号思考和自我中心；具体运算阶段（7-11岁）能对具体事件进行逻辑思考；形式运算阶段（11岁以上）能进行抽象推理。
Lev Vygotsky emphasised social interaction and introduced the Zone of Proximal Development (ZPD): the gap between what a child can do independently and what they can achieve with guidance from a more knowledgeable other (MKO). The ZPD formula can be expressed as ZPD = Assisted Performance – Independent Performance. Scaffolding is the temporary support provided by the MKO to bridge this gap.
列夫·维果茨基强调社会互动，提出了最近发展区（ZPD）：儿童独立完成与他人在有知识者指导下所能达到的水平之间的差距。ZPD 的公式可表示为 ZPD = 辅助完成的成绩 – 独立完成的成绩。支架是在有知识者提供的临时支持，以弥合这一差距。
10. Personality: Eysenck’s PEN Model and the Big Five | 人格：艾森克 PEN 模型与大五人格
Hans Eysenck proposed the PEN model, comprising three super-traits: Psychoticism, Extraversion, and Neuroticism. Extraversion relates to sociability and cortical arousal; neuroticism to emotional instability and reactivity of the limbic system; psychoticism to aggressiveness and impulse control. These dimensions have biological bases and are relatively stable.
汉斯·艾森克提出了 PEN 模型，包含三个人格超级特质：精神质（Psychoticism）、外倾性（Extraversion）和神经质（Neuroticism）。外倾性与社交性和皮层唤醒有关；神经质与情绪不稳定性和边缘系统反应性有关；精神质与攻击性和冲动控制有关。这些维度有生物学基础且较为稳定。
The Big Five model (OCEAN) describes personality using five broad dimensions: Openness to experience, Conscientiousness, Extraversion, Agreeableness, and Neuroticism. Each trait lies on a continuum and predicts behaviour patterns. No single “formula” defines personality, but trait theories provide a framework for measuring individual differences.
大五人格模型（OCEAN）用五个广泛维度描述人格：开放性（Openness）、尽责性（Conscientiousness）、外倾性（Extraversion）、宜人性（Agreeableness）和神经质（Neuroticism）。每种特质居于一个连续体上，可预测行为模式。虽然没有单一“公式”定义人格，但特质理论为测量个体差异提供了框架。
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